f stops

Forgive me, but this the teacher in me coming out after I explained this to someone this morning and remembered some of the questions I've seen here.

An f stop is actually a length. It is the focal length of the lens divided by a number. Thus, for a 100 mm lens, f/2 = 100mm/2 = 50mm. So f/2 for a 50mm lens is 25mm, or one inch; for a 400mm lens it is 200mm, or about 8 inches. That is why long lenses are also fat (and why there aren't many 400mm f/2 lenses around!) and why a bigger f number means you're getting less light through the lens and hence need a slower shutter speed or higher ISO to compensate.

Where do those numbers come from? Each f stop lets in half as much light as the previous one, and since the amount of light a lens lets in is proportional to its area, which is proportional to the square of its diameter, the linear dimension of the f stop is proportional to the square root of its diameter. So to get half the light, you cut the area in half, and the diameter by 1/the square root of 2, or about 1/1.4.

So you get the familiar series of f stops, each of which lets in half as much light as the previous one: f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, and so on.